Question

find the value of x.

Explanation:

Step1: Find the adjacent - interior angle to 142°

The adjacent - interior angle and 142° form a linear pair. So, the adjacent - interior angle is $180 - 142=38^{\circ}$.

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In the triangle, we have $x + 102+38 = 180$.
Simplify the left - hand side: $x+140 = 180$.
Subtract 140 from both sides: $x=180 - 140$.

Answer:

$x = 40$